Table of Contents

Non-Inverting Operational Amplifier: Working Principle and Gain Formula

Non-inverting op amp circuit with Vin, Vout, Rf, Rg, and gain formula Av = 1 + Rf/Rg

A non-inverting operational amplifier is an op amp circuit where the input signal is applied to the non-inverting input, so the output keeps the same polarity as the input. The common closed-loop gain equation is Av = 1 + Rf/Rg. In real circuits, useful gain also depends on supply voltage, input common-mode range, output swing, bandwidth, slew rate, offset, noise, load, and stability.

Use this guide when you need to understand the non-inverting amplifier formula, design a voltage follower or gain stage, or compare this circuit with other op amp configurations. For broader device selection and sourcing, see the Operational Amplifier ICs category.

Quick Take

ItemPractical Answer
Circuit typeVoltage amplifier with the signal applied to the op amp's non-inverting input
Output phaseSame polarity as the input signal
Gain formulaAv = 1 + Rf/Rg
Minimum closed-loop gain1, also called a voltage follower or unity-gain buffer
Main design advantageVery high input impedance compared with many inverting configurations
Main design riskChoosing an op amp whose input/output voltage range, GBW, slew rate, or stability does not fit the real circuit
Related circuitInverting Operational Amplifier

What Is a Non-Inverting Operational Amplifier?

Negative feedback and virtual short concept in a non-inverting op amp circuit
Negative feedback keeps the two op amp input voltages close together while the device remains in its linear operating region.

A non-inverting operational amplifier is a negative-feedback op amp circuit that amplifies a signal without reversing its polarity. The input signal is connected to the + input terminal. A resistor feedback network returns part of the output voltage to the - input terminal, forcing the op amp to adjust its output until the inverting input closely matches the non-inverting input.

This behavior is often summarized by the virtual-short concept: when an op amp operates in its linear region with negative feedback, the two input terminals sit at nearly the same voltage. They are not physically shorted, and the approximation is only valid while the op amp has enough output swing, supply headroom, bandwidth, and loop stability.

This makes the circuit useful for sensor interfaces, buffer stages, active filters, audio preamplifiers, data-acquisition front ends, and power-supply feedback paths. The feedback network sets the ideal closed-loop gain, while the selected op amp's electrical limits decide whether the circuit can produce that gain accurately.

Non-Inverting Amplifier Circuit and Gain Formula

Non-inverting operational amplifier gain formula diagram showing Rf, Rg, Vin, and Vout
The resistor ratio between Rf and Rg sets the ideal closed-loop gain of the basic non-inverting amplifier.

The basic circuit uses two resistors:

SymbolRole in the Circuit
RfFeedback resistor from output to the inverting input
RgGain-setting resistor from the inverting input to ground or a reference node
VinSignal applied to the non-inverting input
VoutAmplified output voltage

For the ideal circuit operating in its linear region, the closed-loop voltage gain is:

Av = Vout / Vin = 1 + Rf / Rg

If Rf = 9 kOhm and Rg = 1 kOhm:

Av = 1 + 9 kOhm / 1 kOhm = 10

A 100 mV input signal would therefore ideally produce a 1 V output signal, provided the op amp supply voltage, input range, output swing, bandwidth, slew rate, and load current allow it.

Why the Gain Is Always 1 or Higher

The +1 term in the gain equation is the key difference between a non-inverting amplifier and an inverting amplifier. In a non-inverting circuit, the feedback divider samples the output and applies a fraction of it to the inverting input. To make the inverting input nearly equal to the non-inverting input, the output must be larger than the input by the divider ratio.

Because Rf/Rg cannot be negative in the normal resistor-divider configuration, the closed-loop gain of this basic non-inverting circuit cannot be less than 1. If attenuation is required, use a divider before the buffer, a different active topology, or another signal-conditioning approach.

Unity-Gain Buffer: The Special Case

Voltage follower op amp buffer with Av equals 1, high input impedance, and low output impedance
A voltage follower uses direct negative feedback to provide unity voltage gain and impedance isolation.

When the output is connected directly to the inverting input, the circuit becomes a voltage follower:

Av = 1

This is also called a unity-gain buffer or buffer amplifier. It does not increase voltage amplitude, but it can isolate a high-impedance source from a lower-impedance load.

Use a voltage follower when the signal level is already correct but the source cannot drive the next stage directly. Common examples include sensor outputs, ADC driver pre-stages, reference-voltage buffering, and signal-conditioning paths where the next circuit must not load the previous one.

Before choosing an op amp for a buffer, confirm that the device is unity-gain stable. Not every op amp is stable at a closed-loop gain of 1, especially some high-speed or decompensated amplifiers.

Non-Inverting vs Inverting Op Amp

Comparison of non-inverting and inverting op amp circuits with gain formulas and phase behavior
Non-inverting and inverting amplifiers differ in phase, input impedance, and gain relationship.
Comparison PointNon-Inverting AmplifierInverting Amplifier
Input connectionSignal enters the non-inverting inputSignal enters through a resistor into the inverting node
Output phaseSame polarity as inputInverted polarity
Basic gain formulaAv = 1 + Rf/RgAv = -Rf/Rin
Minimum gain1 in the basic configurationMagnitude can be below, equal to, or above 1
Input impedanceVery high at the op amp inputMainly set by the input resistor
Typical useBuffering, sensor gain, high-impedance signal amplificationSumming, scaling, signal inversion, controlled input impedance

The better circuit depends on the signal source, required polarity, impedance target, noise target, and system architecture. For the full inverting topology, see the Inverting Operational Amplifier guide.

How to Choose Resistor Values

The ratio of Rf to Rg sets gain, but the absolute resistor values still matter. Very low resistor values increase current and load the output. Very high values increase thermal noise, bias-current error, and susceptibility to leakage or PCB contamination.

Design TargetTypical DirectionWhat to Verify
Low noiseAvoid unnecessarily high resistor valuesResistor noise, op amp voltage noise, source impedance
Low powerAvoid unnecessarily low resistor valuesDivider current and battery budget
Precision DC gainUse tight-tolerance, low-drift resistorsGain error across temperature
High-impedance sourceKeep input bias-current error lowOp amp input bias current and input-protection leakage
High-speed signalKeep parasitics and layout under controlStability, capacitance at the inverting node, feedback layout

For many general-purpose circuits, resistor values in the kilo-ohm to tens-of-kilo-ohm range are a common starting point, then the network is adjusted for noise, power, bias-current error, and stability. Precision or high-speed designs should be validated against the op amp datasheet and layout guidance.

Op Amp Limits to Check in the Datasheet

Op amp datasheet limits for supply range, input common-mode range, output swing, GBW, slew rate, offset, bias, and load stability
The gain formula is only the first step; the selected op amp must also meet the real voltage, speed, load, and stability requirements.
ParameterWhy It MattersDesign Check
Supply voltage rangeThe op amp must operate from the available railsConfirm single-supply or dual-supply operation
Input common-mode rangeThe non-inverting input must stay inside the valid input rangeRail-to-rail input may be needed in low-voltage systems
Output swingThe output must reach the required voltage without clippingCheck headroom at the expected load current
Gain bandwidth productHigher closed-loop gain reduces usable bandwidthConfirm GBW margin at the target gain
Slew rateLimits large-signal output speedImportant for audio, waveform, and fast sensor signals
Input offset voltageCreates DC output errorCritical for precision sensor and measurement circuits
Input bias currentCreates error with source and feedback resistancesUse low-bias input types when source impedance is high
NoiseAffects small-signal accuracy and audio qualityCompare voltage noise and current noise with source impedance
Load driveThe output must drive the next stage or loadCheck output current and capacitive-load stability
Package and pinoutMust fit the PCB and assembly processConfirm exact package code and pinout
LifecycleAffects long-term production and replacement decisionsVerify the exact orderable part before BOM release

Typical Applications

ApplicationWhy the Circuit Is UsefulKey Op Amp Checks
Sensor signal conditioningAmplifies a sensor voltage without heavily loading the sourceBias current, offset voltage, noise, input common-mode range
Voltage reference bufferIsolates a reference node from downstream load changesOutput current, stability, offset, noise
Audio preamplifierProvides voltage gain while preserving signal polarityNoise, distortion, slew rate, supply voltage
ADC driver front endScales and buffers a signal before conversionOutput swing, settling time, bandwidth, input range
Active filter stageCombines gain with frequency shapingGBW, slew rate, noise, resistor/capacitor tolerance
Power feedback circuitConditions error or feedback signalsSupply range, output swing, stability, temperature drift

Example Design Check Flow

  1. Define the required closed-loop gain using Av = 1 + Rf/Rg.
  2. Confirm the maximum input signal and calculate the required output swing.
  3. Check whether the supply rails give enough input common-mode and output headroom.
  4. Estimate signal frequency and confirm GBW margin at the selected gain.
  5. Check slew rate for the largest expected output waveform.
  6. Review offset voltage, bias current, and noise against the error budget.
  7. Confirm load current and capacitive-load stability.
  8. Check package, pinout, and layout guidance before moving from simulation to PCB.
  9. Compare other topologies if the circuit needs inversion, summing, filtering, or attenuation.
  10. Verify the exact op amp model and manufacturer datasheet before BOM release.

Common Mistakes

Mistake 1: Treating the Formula as the Whole Design

Av = 1 + Rf/Rg gives the ideal closed-loop gain. It does not guarantee that the output can swing to the required voltage, that the amplifier has enough bandwidth, or that the circuit is stable with the selected load and PCB layout.

Mistake 2: Forgetting Input and Output Voltage Limits

Many op amps cannot sense all the way to both supply rails, and many cannot drive their output fully to both rails under load. Even a rail-to-rail device still needs its datasheet limits checked at the expected load current.

Mistake 3: Assuming Any Op Amp Works as a Buffer

A unity-gain buffer requires an op amp that is stable at a closed-loop gain of 1. If the datasheet specifies a minimum stable gain greater than 1, do not use that part as a voltage follower.

Mistake 4: Replacing an Op Amp by Package Alone

Two op amps in the same package are not automatically interchangeable. Pinout, supply range, input common-mode range, output swing, noise, offset, GBW, slew rate, load drive, temperature grade, and lifecycle can all affect compatibility.

Related Op Amp Guides

FAQ

What is a non-inverting operational amplifier?

A non-inverting operational amplifier is an op amp circuit where the input signal is applied to the non-inverting input and negative feedback sets a closed-loop gain while keeping the output in phase with the input.

What is the gain formula for a non-inverting op amp?

The ideal closed-loop gain is Av = 1 + Rf/Rg, where Rf is the feedback resistor and Rg is the resistor from the inverting input to ground or a reference node.

Can a non-inverting amplifier have a gain below 1?

The basic non-inverting configuration has a minimum gain of 1. If attenuation is required, use a resistor divider, another amplifier topology, or a different signal-conditioning approach.

What is a voltage follower?

A voltage follower is a unity-gain non-inverting buffer. Its voltage gain is 1, but it provides impedance isolation between a signal source and the next circuit stage.

Which op amp should I choose for a non-inverting amplifier?

Choose the op amp by supply voltage, input common-mode range, output swing, GBW, slew rate, offset voltage, bias current, noise, load drive, package, and lifecycle. The gain formula alone is not enough for part selection.

Can I replace one op amp with another in the same package?

Not automatically. Check pinout, electrical limits, supply range, input/output range, bandwidth, slew rate, noise, offset, temperature grade, and lifecycle before approving an alternative.

Request Quote or Submit BOM

If your design uses a non-inverting amplifier or voltage follower, include the exact op amp part number if known, package, quantity, supply rails, required gain, input signal range, output load, and signal frequency.

Use Send Inquiry for a known part number or a multi-line BOM. Stock, price, lead time, lifecycle, compliance, and replacement suitability should be verified during the quote review.

References and Further Reading